ticle permeability as in convective chromatographic media (Figure 1). The use of flow-through particles (Figure 2) has been increasing recently in relation to protein separation by HPLC with perfusive chromatography. Intraparticle forced convection is a mass transport mechanism which, in addition to diffusive transport, cannot be neglected in large pore materials. The key concept to be retained is the augmented diffusivity by convection, which explains why the efficiency of adsorptive processes is improved with convective chromatographic media.

The effect of intraparticle convective flow due to a total pressure gradient was quantified in 1982 by a group measuring effective diffusivities by chromatographic techniques. The analysis of experimental results was first made with a conventional model which included an apparent diffusion (lumping diffusion and convection) of tracer inside pores. The apparent diffusivity was found to increase with the superficial velocity. From the equivalence of the conventional model and a detailed model which allows for the separate contribution of diffusive and convective flow (Figure 3) the apparent diffusivity or augmented diffusivity by convection, De was calculated for an inert tracer as a function of the true effective diffusivity

De and the intraparticle mass Peclet number A:

where:

A tanhA A

The intraparticle Peclet number, X, is the ratio between the time constant for pore diffusion, td, and the time constant for intraparticle convection, tc. For slab geometry, td = sp12/De and Tc = gp1/v0 so X = v01/De where 1 is the half-thickness of the slab particle and v0 is the intraparticle convective velocity inside large pores; for sphere geometry with particle radius Rp, the diffusion time constant is td = spRp/De = Rp/Dp and X = VoRp/3De.

The enhancement of diffusivity by intrapar-ticle convection is 1/f(X) = De/De and so the apparent diffusion time constant fd = td f(X). Figure 4 shows the enhancement factor De/De as a function of the intraparticle Peclet number X. At low bed superficial velocities, u0, the convective velocity inside pores, v0, is also small; therefore f(X) = 1 and De = De (diffusion-controlled case); at high superficial velocities u0, and therefore high v0 and high X,

Figure 2 An example of permeable or flow-through chromatographic media with large pores and gel microspheres.

f(X) = 3/k; the augmented diffusivity is De = v01 /3 for slab geometry and De = v0Rp/9 for spheres (convection-controlled case), which depends only on the particle permeability, fluid viscosity and pressure drop across the particle.

Global warming is a huge problem which will significantly affect every country in the world. Many people all over the world are trying to do whatever they can to help combat the effects of global warming. One of the ways that people can fight global warming is to reduce their dependence on non-renewable energy sources like oil and petroleum based products.